Question 119807
Start with the given system

{{{x+21=-2y}}}
{{{y=3x}}}




{{{x+21=-2(3x)}}}  Plug in {{{y=3x}}} into the first equation. In other words, replace each {{{y}}} with {{{3x}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{x+21=-6x}}} Multiply



{{{x=-6x-21}}}Subtract 21 from both sides



{{{x+6x=-21}}} Add 6x to both sides



{{{7x=-21}}} Combine like terms on the left side



{{{x=(-21)/(7)}}} Divide both sides by 7 to isolate x




{{{x=-3}}} Divide





Now that we know that {{{x=-3}}}, we can plug this into {{{y=3x}}} to find {{{y}}}




{{{y=3(-3)}}} Substitute {{{-3}}} for each {{{x}}}



{{{y=-9}}} Simplify



So our answer is {{{x=-3}}} and {{{y=-9}}}